If I were you, I would clarify with your client that you wish to change the name of the company. This is typically NOT part of a re-branding process.
He may under the assumption that you're just redesigning his logo with the existing name... which would make for a whole lot of work on your part for nothing if he doesn't actually want to change the name.
If a company rename is part of the process, keep in mind that it's not as simple as just picking a new name. A professional would also check for trademark registration conflicts, check to see if a corresponding domain name is available, social media names, etc...